@Article{AAMM-10-5,
author = {Yang, Yan and Zhang, Shiquan},
title = {Mixed Finite Element Methods for Elastodynamics Problems in the Symmetric Formulation},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2018},
volume = {10},
number = {5},
pages = {1279--1304},
abstract = {<p style="text-align: justify;">In this paper, we analyze semi-discrete and fully discrete mixed finite element
methods for linear elastodynamics problems in the symmetric formulation. For
a large class of conforming mixed finite element methods, the error estimates for each
scheme are derived, including the energy norm and $L^2$ norm for stress, and the $L^2$ norm for velocity. All the error estimates are robust for the nearly incompressible materials,
in the sense that the constant bound and convergence order are independent
of Lamé&nbsp;constant λ. The stress approximation in both norms, as well as the velocity
approximation in $L^2$ norm, are with optimal convergence order. Finally numerical
experiments are provided to confirm the theoretical analysis.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2017-0280},
url = {https://global-sci.com/article/73223/mixed-finite-element-methods-for-elastodynamics-problems-in-the-symmetric-formulation}
}